Logics and Calculuses
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First published Wed Jun 17, 1998; substantive revision Mon Mar 26, 2012 Relevance logics are non-classical logics. Called ‘relevant logics’ in Britain and Australasia, these systems developed as attempts to avoid the paradoxes of material and strict implication.
First published Thu Jul 6, 2006; substantive revision Thu Jan 27, 2011 There is an obvious difference between what a term designates and what it means. At least it is obvious that there is a difference. In some way, meaning determines designation, but is not synonymous with it. After all, “the morning star” and “the evening star” both designate the planet Venus, but don't have the same meaning. Intensional logic attempts to study both designation and meaning and investigate the relationships between them.
First published Thu Dec 20, 2007; substantive revision Wed Mar 4, 2009 Second-order logic is an extension of first-order logic where, in addition to quantifiers such as “for every object (in the universe of discourse),” one has quantifiers such as “for every property of objects (in the universe of discourse).” This augmentation of the language increases its expressive strength, without adding new non-logical symbols, such as new predicate symbols. For classical extensional logic (as in this entry), properties can be identified with sets, so that second-order logic provides us with the quantifier “for every set of objects.” There are two approaches to the semantics of second-order logic.
First published Wed Jan 4, 2006 Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry. 1.
First published Tue Feb 7, 2006; substantive revision Wed Apr 21, 2010 Deontic logic [ 1 ] is that branch of symbolic logic that has been the most concerned with the contribution that the following notions make to what follows from what: To be sure, some of these notions have received more attention in deontic logic than others. However, virtually everyone working in this area would see systems designed to model the logical contributions of these notions as part of deontic logic proper. As a branch of symbolic logic, deontic logic is of theoretical interest for some of the same reasons that modal logic is of theoretical interest. However, despite the fact that we need to be cautious about making too easy a link between deontic logic and practicality, many of the notions listed are typically employed in attempting to regulate and coordinate our lives together (but also to evaluate states of affairs).
Predicate Logic The propositional logic is not powerful enough to represent all types of assertions that are used in computer science and mathematics, or to express certain types of relationship between propositions such as equivalence. For example, the assertion "x is greater than 1", where x is a variable, is not a proposition because you can not tell whether it is true or false unless you know the value of x. Thus the propositional logic can not deal with such sentences. However, such assertions appear quite often in mathematics and we want to do inferencing on those assertions. Also the pattern involved in the following logical equivalences can not be captured by the propositional logic:
First published Sat Sep 16, 2000; substantive revision Mon Nov 2, 2009 Typically, a logic consists of a formal or informal language together with a deductive system and/or a model-theoretic semantics. The language is, or corresponds to, a part of a natural language like English or Greek. The deductive system is to capture, codify, or simply record which inferences are correct for the given language, and the semantics is to capture, codify, or record the meanings, or truth-conditions, or possible truth conditions, for at least part of the language.
First published Sat Mar 18, 2000; substantive revision Wed Mar 23, 2011 Aristotle's logic, especially his theory of the syllogism, has had an unparalleled influence on the history of Western thought. It did not always hold this position: in the Hellenistic period, Stoic logic, and in particular the work of Chrysippus, took pride of place. However, in later antiquity, following the work of Aristotelian Commentators, Aristotle's logic became dominant, and Aristotelian logic was what was transmitted to the Arabic and the Latin medieval traditions, while the works of Chrysippus have not survived. This unique historical position has not always contributed to the understanding of Aristotle's logical works.
Submitted by Richard Zach on November 7, 2008 - 2:28pm. David Chalmers and David Bourget are setting up a new online resource for papers in philosophy, for which they're designing a taxonomy of philosophical topics to be used for classifying papers in the database. David asks For now, I'm calling for feedback from the philosophical community, either via e-mail or via comments on this blog. Especially valuable will be thoughts on categories that we've missed, on ways to structure categories that don't yet have much structure, and on better ways of structuring things in tricky cases. Please post responses at Dave's blog .
Reaching Good Conclusions without Being Precise AITopics > Reasoning > Qualitative Reasoning "Broadly speaking, qualitative-reasoning research aims to develop representation and reasoning techniques that will enable a program to reason about the behavior of physical systems, without the kind of precise quantitative information needed by conventional analysis techniques such as numerical simulators. ... Observing pouring rain and a river's steadily rising water level is sufficient to make a prudent person take measures against possible flooding - without knowing the exact water level, the rate of change, or the time the river might flood." - Yumi Iwasaki Introductory Readings Kenneth D.
First published Tue Feb 29, 2000; substantive revision Fri Oct 2, 2009 A modal is an expression (like ‘necessarily’ or ‘possibly’) that is used to qualify the truth of a judgement. Modal logic is, strictly speaking, the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that’. However, the term ‘modal logic’ may be used more broadly for a family of related systems.
14.1.1 Situation Calculus The idea behind situation calculus is that (reachable) states are definable in terms of the actions required to reach them. These reachable states are called situations. What is true in a situation can be defined in terms of relations with the situation as an argument.
Next: Simple situation calculus Up: ELABORATION TOLERANCE Previous: Formalizing the Amarel Representation Situation Calculus Representations The term situation calculus is used for a variety of formalisms treating situations as objects, considering fluents that take values in situations, and events (including actions) that generate new situations from old. At present I do not know how to write a situation calculus formalization that tolerates all (or even most) of the elaborations of section 7 .
Introduction to Logic: People often incorrectly say things like " that's illogical ", or " the only logical thing to do ". Of course, as part of common parlance , we all know exactly what they mean, but in the world of logic, their statements are erroneous. For instance the man who supports Manchester United one week, then switches allegiance to Manchester City the next, is fickle, but he may not be illogical .
This is a list of rules of inference , logical laws that relate to mathematical formulae. [ edit ] Introduction Rules of inference are syntactical transform rules which one can use to infer a conclusion from a premise to create an argument. A set of rules can be used to infer any valid conclusion if it is complete, while never inferring an invalid conclusion, if it is sound. A sound and complete set of rules need not include every rule in the following list, as many of the rules are redundant, and can be proven with the other rules. Discharge rules permit inference from a subderivation based on a temporary assumption.